Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods

Zhao Jun Bai*, Ren Cang Li, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The locally optimal block preconditioned 4-d conjugate gradient method (LOBP4dCG) for the linear response eigenvalue problem was proposed by Bai and Li (2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li (2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4dCG (ELOBP4dCG). Numerical results of the ELOBP4dCG strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.

Original languageEnglish
Pages (from-to)1443-1460
Number of pages18
JournalScience China Mathematics
Volume59
Issue number8
DOIs
StatePublished - 1 Aug 2016

Keywords

  • conjugate-gradient
  • deflation
  • eigenvalue problem
  • linear response

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